Fast iterative solvers for boundary value problems on a local spherical region

Quoc Thong Le Gia, Thanh Tran


Boundary value problems on local spherical regions arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Meshless methods using radial basis functions provide a simple way to construct numerical solutions with high accuracy. However, the linear systems arising from these methods are usually ill-conditioned, which poses a challenge for iterative solvers. We construct preconditioners based on an additive Schwarz method to accelerate the solution process for solving boundary value problems on local spherical regions.

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boundary value problem, unit sphere, additive Schwarz method

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